Questions tagged [quantum-chemistry]
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220
questions
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Atomic density derivative with respect to nuclear coordinates transformed to all space
Please show that the derivative of some atomic density $\rho_{I}$ with respect to its nuclear coordinate $R_{I}$ can be expressed in terms of its electronic coordinate $|\textbf{r - R}_I|$
$ \frac{\...
2
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1answer
32 views
Hydrogen bonding under quantum mechanics
I know that Fermi-Dirac statistics can be used to account for covalent bonding, but how does quantum mechanics explain hydrogen bonding?
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2answers
55 views
How to interpret Hamiltonian in terms of its matrix representation
I am reading a research paper (A Theoretical Analysis of Zero Field Splitting Parameters of Mn2+ Doped Diglycine Calcium Chloride Tetrahydrate) where they state the Hamiltonian term:
$$H=\frac{F}{180}\...
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0answers
16 views
Is the $g$-tensor describing the Zeeman effect for molecules always diagonalizable?
The Zeeman splitting of a molecule can be described through the $g$-tensor, which couples the magnetic field to the angular momentum of the molecule. Is the $g$-tensor always diagonalizable?
2
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1answer
19 views
Degree of kinetic energy component in Hamiltonian for any molecule
In reading "Density functional theory of atoms and molecules" by Parr and Yang, I was not sure what is meant by this sentence when the Virial theorem was introduced.
Suppose I have a ...
3
votes
1answer
88 views
Casimir effect evidence
How does the attraction between two metal plates support a new effect (or force)?
Isn't it expected that two plates attract each other due to the London dispersion?
If so, how does the experiment ...
2
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1answer
37 views
Hybrid Orbitals
https://glossary.periodni.com/glossary.php?page=41&en=high+fructose pictures like the ones in this article make no sense to me.
I understand that we can take solutions to the Schrödinger equation ...
0
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2answers
32 views
Why do elements want to mimic Nobel gasses so much? [duplicate]
Why is the octet rule true?
How can electrons even stay around nuclei with lesser number of protons?
4
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1answer
66 views
How does the Pauli Exclusion principle explain the incompressibility of metals?
The Pauli Exclusion principles states that no two identical fermions can have the same quantum state. In my lecture notes, it is mentioned that this principle helps us explain the fact that metals are ...
1
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1answer
26 views
Expression and explanation of quantum mechanical harmonic oscillator
I am currently studying the textbook Infrared and Raman Spectroscopy, 2nd edition, by Peter Larkin. In a section entitled Quantum Mechanical Harmonic Oscillator, the author says the following:
Fig. 2....
0
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1answer
37 views
Hamiltonian matrix elements involving ladder operators for spin-1 state
I am reading the Doctorate thesis 'Zero-Field Anisotropic Spin Hamiltonians in First-Row
Transition Metal Complexes: Theory, Models and
Applications' (link: https://tel.archives-ouvertes.fr/tel-...
1
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0answers
23 views
Two descriptions of Valence Bond Theory
I am trying to understand theoretically Valence Bond Theory from the first principles of Quantum Mechanics and suitable approximations. I am a mathematician with shaky bases in Quantum Mechanics.
...
0
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1answer
45 views
Is the $1s^22s^22p^6$ atomic configuration lower in energy than the $1s^22s^22p^5$ atomic configuration?
I read that atoms in the first few rows of the periodic table gain or lose electrons to have 8 valence electrons so that they are energetically stable and has minimum energy.
This means that an atom ...
1
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1answer
45 views
Interpretation of occupation numbers and creation-annihilation operators in strongly correlated systems
I hope I am not asking anything stupid, but I am having a hard time interpreting some
(seemingly simple) results.
The simplest approximate form of an $N$-electron wave function (w.f.) is a Slater-...
2
votes
1answer
37 views
Unitary Coupled Cluster Operator
In quantum computing, we always want to deal with unitary evolution operators. That's why the traditional definition of the Coupled Cluster ansatz is modified to the so-called Unitary Coupled Cluster, ...
0
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1answer
69 views
Benzene ground state
I’m currently studying my first course on Quantum Physics. Regarding the topic of Sommerfeld’s quantization rules, I’ve come across a problem where I was asked whether a benzene molecule would require ...
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0answers
30 views
Calculation of atomic spectrum
I need to calculate spectrum of Hg atom (wavelength and transition intensity), taking into account relativistic corrections. Can someone suggest a software or a package for atomic spectroscopy, that I ...
0
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0answers
19 views
Existence of higher derivatives of molecular potential energy surfaces
I would like to know if anything is known about the mathematical regularity properties (continuity and existence/continuity of higher derivatives) of the (exact) Born-Oppenheimer potential energy ...
2
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3answers
132 views
What are the $sp^3$ orbital bond directions relative to a Cartesian reference frame?
When I try to search for this, I find images like below, but it is not clear to me what the actual bond directions are, i.e. the first one appears to be (0, 0, 1) but then I am not sure of the others.
2
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1answer
39 views
Quantitative contribution of kinetic and potential energies to the binding energy of the $\sigma$ orbital in $\text{H}_2$ or $\text{H}_2^+$
When a hydrogen molecule forms, 4.52 eV of energy is released, while for $\text{H}_2^+$ the binding energy is 2.77 eV. Such a binding energy is the difference of energies that have four terms in them: ...
4
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4answers
178 views
Why does orbital overlap cause attraction?
I have been taught that when orbitals overlap as in $\sigma$ and $π$ bonds, the formation of a bond (which is basically an attraction) takes place. Why does this cause attraction, shouldn't they repel?...
1
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1answer
66 views
How to calculate the second order pertubation in an electron gas?
This problem is from the book Quantum theory of many particles systems by Fetter & Walecka (1971), exercise 1.4.
Problem discription:
The Hamiltonian could be divided into $$H_0=\sum_\limits{\...
4
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2answers
194 views
Can you explain DFT and TDDFT functioning (math aside)?
I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT and Time-Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...
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0answers
25 views
Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?
Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity)
Theoretical ...
0
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2answers
68 views
Is it the Coulomb force which acts between electron and protons creating chemical bonds?
When calculating forces on the atomic level, although Quantum mechanics makes the positions of charged particles"smeared out" is it the Coulomb force which is acting between smeared out electrons and ...
1
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0answers
66 views
Coulomb Barrier - Nuclear Physics
When we calculate the Coulomb's barrier we usually assume that two nucleus (target and projectile) just touch each other so the barrier:
$$E_{cb}=\frac{0.96Z_1 Z_2}{A_1 ^{1/3}+A_2^{1/3}}\text{ MeV} \...
3
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5answers
581 views
How can the mechanism of electrons in an atom be explained? [closed]
I am a high school student who takes both Physics and Chemistry.
Recently I learnt about the quantum mechanical point of view of looking at electrons or nuclei. I also learnt that the wave functions ...
7
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1answer
181 views
DFT: When would one use a LDA over a GGA method?
Computationally using Density Functional Theory (DFT), is there any examples where Local Density Approximation (LDA) would be preferred over using Gradient Generalized Approximation (GGA) methods for ...
1
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0answers
39 views
Ground state term symbol, why is $L = |M_L|$, if $L$ must be a maximum?
I'm trying to understand how to predict ground state term symbol of atoms.
After finding the biggest S, why the biggest $L$ will be $L = |M_L|$, where $M_L = \sum m_l$?
I know this rule works to ...
8
votes
1answer
136 views
Does the hydrogen anion have bound excited states?
I'm having some trouble puzzling out the literature regarding the existence of bound excited states in the hydrogen anion, H$^-$.
Wikipedia claims that no such states exist, and that the subject is ...
2
votes
2answers
248 views
Is there a limit of electrons a single hydrogen atom can have?
Is there a limit of electrons a single hydrogen atom can have? If so what is it? why? Is the the answer to why scalable to helium?
0
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0answers
32 views
Why do all atoms follow the same $n$ and $\ell$ quantization conditions as hydrogen? [duplicate]
The quantum state of an electron in a hydrogen atom is specified by 4 quantum numbers: $n$ , $\ell$, $m_\ell$, $m_s$ which can take the following values:
$$n = 1, 2, 3, ... $$
$$\ell = 0, 1, 2, 3, ......
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Can Hartree-Fock-Bogoliubov be used for dynamics?
I am aware of Hartree-Fock as both a tool to find interacting ground states for fermionic systems (eg the Roothan self-consistent field procedure). One way of deriving the ground state method is to ...
0
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0answers
14 views
What (in silico information) defines the transfer function of a Quantum Amplifier, in the form of a molecule?
Let’s say a team of scientists have published the structure of a molecule they claim acts as a quantum amplifier.
Photons travel along a quantum channel carrying qubits in their polarization. The ...
2
votes
1answer
44 views
On diagonal terms in the Coulomb matrix
I have seen many machine learning algorithms for prediction of quantum chemistry properties that use Coulomb matrix as their input. Coulomb matrix is defined as
$$\boldsymbol{M}_{i j}^{\mathrm{...
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17 views
Calculating Simple Ground State Energy Of Hydrogen From Geminal Spin Function
I'm very new to quantum stuff and I'm experimenting, but I'd like a good explanation here if you can give it.
Here's the circuit diagram and the results.
I'm seeing from this paper that you can get ...
2
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0answers
30 views
What exactly does it mean for an element to experimentally violate the Madelung ordering rule?
The Madelung ordering rule says that as you increase the atomic number of a neutral atom, the electron orbitals fill up in order of increasing value of $n+l$, and in increasing order of $n$ within a ...
1
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1answer
81 views
What is $\frac{d}{d\psi}\langle\psi| \hat{O} | \psi\rangle$?
I would like to know what is the derivative of an expectation value with respect to the molecular state
$$\frac{d}{d\psi}\langle\psi| \hat{\mathbf{O}} | \psi\rangle$$
Note that here $|\psi\rangle$ ...
0
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1answer
159 views
The overlap of two Slater determinant states
Suppose I have two fermionic number states in different bases, with the same particle number $N$ - call them $|\Psi\rangle$ and $|\Phi\rangle$. In the position basis, I can write the many-body ...
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0answers
24 views
In what cases do isotopes cause non-negligible effects in chemicals
For example, CO2 (carbon dioxide), there could be Carbon8-Carbon22 isotopes, and I'm not sure for oxygen. Wondering at what point there is some sort of non-negligible effect, and what the effect(s) ...
0
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1answer
35 views
Band formation in diamond
Why is it that in the band diagram of diamond does the sp3 hybridised orbital split into two forming valence band and conduction band?
I thought that these sp3 hybridised orbital forms 4n bonding and ...
3
votes
2answers
126 views
What is a nuclear wave packet?
What is the definition of a nuclear wave packet ? I often see the term used but i don't know how it is defined. It seems to be connected to the Born-Oppenheimer approximation. Is it defined there and ...
1
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2answers
182 views
What's meaning of velocity of electron? [closed]
How do we define velocity of microscopic particles at small scales. As for macroscopic particle we can scale the distance travelled by object. But this is not the case with electron.
Still, while ...
2
votes
2answers
140 views
What is the simplest possible Hamiltonian that yields an Antisymmetric Wavefunction?
I am using a Split-Operator Fourier Transform (SOFT) technique to solve the time-dependent electronic Schrödinger Equation (TDSE) for a Hydrogen molecule under the Born-Oppenheimer approximation. So I ...
1
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1answer
227 views
$sp^3$ Hybridization wavefunctions and probability density
I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this:
I can plot 4 overlapping probability densities in a tetrahedral shape:
So far it looks OK.
But when I'm ...
0
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1answer
227 views
1D Infinite Square Well: Box Suddenly Increase in Size. Why the coefficients can be derived by inner producting the wave functions?
I have read the question 1D Infinite Square Well: Box Suddenly Increase in Size. How treat this?. There are two key equations in the selected answer.
$$\int_0^{2L} dx \ \psi^*_m\left(x\right) \Psi\...
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2answers
133 views
Basis Functions for Hartree Fock, and Configuration Interaction
I'm about halfway through the book Szabo and Ostlund, and while I think I understand the rough idea of Hartree-Fock and configuration interaction, there is something I would like to clarify.
For one, ...
1
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0answers
23 views
Operator for change of state?
I am trying to model a quantum system that has only three different classical states, so that the Hilbert space is simply $\mathbb C^3$, and let's call its standard basis $e_1,e_2,e_3$, with each of ...
2
votes
1answer
107 views
How to propagate Heller's model of the Gaussian Wave Packet? [closed]
I'm working on an undergraduate research project on gaussian wave packets, but am a pretty big noob in terms of theoretical chemistry and the like. I'm having a lot of difficulty grasping this concept ...
4
votes
3answers
519 views
Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?
I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
